Re: Fix ccos, csin, ccosh, csinh overflows (bug 14123)

[David Miller <davem at davemloft dot net>]

From: "Joseph S. Myers" <joseph@codesourcery.com>
Date: Fri, 18 May 2012 23:10:42 +0000 (UTC)

> Bug 14123 is that ccos, csin, ccosh and csinh have internal overflows
> similar to those I fixed for cexp (bug 13892) and ctan/ctanh (bug
> 11521).  The same technique for fixing them applies: if an overflowing
> sinh or cosh value might be multiplied by a sin or cos value
> (magnitude less than 1) to produce a non-overflowing result, split the
> sinh or cosh computation into multiple non-overflowing exp
> computations.
> 
> I propose this patch fixing these overflows that way.  (Note that ccos
> is implemented in terms of ccosh so does not need fixing separately.)
> Tested x86 and x86_64 and ulps updated accordingly.  Ports note: m68k
> has its own versions of these functions that will need fixing
> similarly.

Joseph could you please integrate the following Sparc ulps update
into your changes?

Thanks.

diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps
index c903087..b4bb1b5 100644
--- a/sysdeps/sparc/fpu/libm-test-ulps
+++ b/sysdeps/sparc/fpu/libm-test-ulps
@@ -580,6 +580,38 @@ double: 1
 idouble: 1
 
 # ccos
+Test "Imaginary part of: ccos (-0.75 + 11357.25 i) == 9.001213196851067077465606717616495588201e4931 + 8.385498349388321535962327491346664141020e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccos (-0.75 + 710.5 i) == 1.347490911916428129246890157395342279438e308 + 1.255317763348154410745082950806112487736e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: ccos (-0.75 + 89.5 i) == 2.708024460708609732016532185663087200560e38 + 2.522786001038096774676288412995370563339e38 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccos (-0.75 + 89.5 i) == 2.708024460708609732016532185663087200560e38 + 2.522786001038096774676288412995370563339e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccos (-0.75 - 11357.25 i) == 9.001213196851067077465606717616495588201e4931 - 8.385498349388321535962327491346664141020e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccos (-0.75 - 710.5 i) == 1.347490911916428129246890157395342279438e308 - 1.255317763348154410745082950806112487736e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: ccos (-0.75 - 89.5 i) == 2.708024460708609732016532185663087200560e38 - 2.522786001038096774676288412995370563339e38 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccos (-0.75 - 89.5 i) == 2.708024460708609732016532185663087200560e38 - 2.522786001038096774676288412995370563339e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "Real part of: ccos (-2 - 3 i) == -4.18962569096880723013255501961597373 - 9.10922789375533659797919726277886212 i":
 ildouble: 1
 ldouble: 1
@@ -596,8 +628,52 @@ ifloat: 1
 Test "Imaginary part of: ccos (0.75 + 1.25 i) == 1.38173873063425888530729933139078645 - 1.09193013555397466170919531722024128 i":
 float: 1
 ifloat: 1
+Test "Imaginary part of: ccos (0.75 + 11357.25 i) == 9.001213196851067077465606717616495588201e4931 - 8.385498349388321535962327491346664141020e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccos (0.75 + 710.5 i) == 1.347490911916428129246890157395342279438e308 - 1.255317763348154410745082950806112487736e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: ccos (0.75 + 89.5 i) == 2.708024460708609732016532185663087200560e38 - 2.522786001038096774676288412995370563339e38 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccos (0.75 + 89.5 i) == 2.708024460708609732016532185663087200560e38 - 2.522786001038096774676288412995370563339e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccos (0.75 - 11357.25 i) == 9.001213196851067077465606717616495588201e4931 + 8.385498349388321535962327491346664141020e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccos (0.75 - 710.5 i) == 1.347490911916428129246890157395342279438e308 + 1.255317763348154410745082950806112487736e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: ccos (0.75 - 89.5 i) == 2.708024460708609732016532185663087200560e38 + 2.522786001038096774676288412995370563339e38 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccos (0.75 - 89.5 i) == 2.708024460708609732016532185663087200560e38 + 2.522786001038096774676288412995370563339e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccos (0x1p-1074 + 1440 i) == inf - 5.981479269486130556466515778180916082415e301 i plus overflow exception":
+double: 1
+idouble: 1
+Test "Imaginary part of: ccos (0x1p-16434 + 22730 i) == inf - 1.217853148905605987081057582351152052687e4924 i plus overflow exception":
+ildouble: 1
+ldouble: 1
 
 # ccosh
+Test "Imaginary part of: ccosh (-11357.25 + 0.75 i) == 9.001213196851067077465606717616495588201e4931 - 8.385498349388321535962327491346664141020e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccosh (-11357.25 - 0.75 i) == 9.001213196851067077465606717616495588201e4931 + 8.385498349388321535962327491346664141020e4931 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: ccosh (-2 - 3 i) == -3.72454550491532256547397070325597253 + 0.511822569987384608834463849801875634 i":
 float: 1
 ifloat: 1
@@ -608,6 +684,32 @@ float: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: ccosh (-710.5 + 0.75 i) == 1.347490911916428129246890157395342279438e308 - 1.255317763348154410745082950806112487736e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccosh (-710.5 - 0.75 i) == 1.347490911916428129246890157395342279438e308 + 1.255317763348154410745082950806112487736e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: ccosh (-89.5 + 0.75 i) == 2.708024460708609732016532185663087200560e38 - 2.522786001038096774676288412995370563339e38 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccosh (-89.5 + 0.75 i) == 2.708024460708609732016532185663087200560e38 - 2.522786001038096774676288412995370563339e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: ccosh (-89.5 - 0.75 i) == 2.708024460708609732016532185663087200560e38 + 2.522786001038096774676288412995370563339e38 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccosh (-89.5 - 0.75 i) == 2.708024460708609732016532185663087200560e38 + 2.522786001038096774676288412995370563339e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "Real part of: ccosh (0.75 + 1.25 i) == 0.408242591877968807788852146397499084 + 0.780365930845853240391326216300863152 i":
 double: 1
 float: 1
@@ -616,6 +718,44 @@ ifloat: 1
 Test "Imaginary part of: ccosh (0.75 + 1.25 i) == 0.408242591877968807788852146397499084 + 0.780365930845853240391326216300863152 i":
 float: 1
 ifloat: 1
+Test "Imaginary part of: ccosh (11357.25 + 0.75 i) == 9.001213196851067077465606717616495588201e4931 + 8.385498349388321535962327491346664141020e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccosh (11357.25 - 0.75 i) == 9.001213196851067077465606717616495588201e4931 - 8.385498349388321535962327491346664141020e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccosh (1440 + 0x1p-1074 i) == inf + 5.981479269486130556466515778180916082415e301 i plus overflow exception":
+double: 1
+idouble: 1
+Test "Imaginary part of: ccosh (22730 + 0x1p-16434 i) == inf + 1.217853148905605987081057582351152052687e4924 i plus overflow exception":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccosh (710.5 + 0.75 i) == 1.347490911916428129246890157395342279438e308 + 1.255317763348154410745082950806112487736e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccosh (710.5 - 0.75 i) == 1.347490911916428129246890157395342279438e308 - 1.255317763348154410745082950806112487736e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: ccosh (89.5 + 0.75 i) == 2.708024460708609732016532185663087200560e38 + 2.522786001038096774676288412995370563339e38 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccosh (89.5 + 0.75 i) == 2.708024460708609732016532185663087200560e38 + 2.522786001038096774676288412995370563339e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: ccosh (89.5 - 0.75 i) == 2.708024460708609732016532185663087200560e38 - 2.522786001038096774676288412995370563339e38 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: ccosh (89.5 - 0.75 i) == 2.708024460708609732016532185663087200560e38 - 2.522786001038096774676288412995370563339e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
 
 # cexp
 Test "Imaginary part of: cexp (-10000 + 0x1p16383 i) == 1.045876464564882298442774542991176546722e-4343 + 4.421154026488516836023811173959413420548e-4344 i":
@@ -1027,26 +1167,166 @@ ildouble: 1
 ldouble: 1
 
 # csin
+Test "Real part of: csin (-0.75 + 11357.25 i) == -8.385498349388321535962327491346664141020e4931 + 9.001213196851067077465606717616495588201e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: csin (-0.75 + 710.5 i) == -1.255317763348154410745082950806112487736e308 + 1.347490911916428129246890157395342279438e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: csin (-0.75 + 89.5 i) == -2.522786001038096774676288412995370563339e38 + 2.708024460708609732016532185663087200560e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csin (-0.75 + 89.5 i) == -2.522786001038096774676288412995370563339e38 + 2.708024460708609732016532185663087200560e38 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: csin (-0.75 - 11357.25 i) == -8.385498349388321535962327491346664141020e4931 - 9.001213196851067077465606717616495588201e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: csin (-0.75 - 710.5 i) == -1.255317763348154410745082950806112487736e308 - 1.347490911916428129246890157395342279438e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: csin (-0.75 - 89.5 i) == -2.522786001038096774676288412995370563339e38 - 2.708024460708609732016532185663087200560e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csin (-0.75 - 89.5 i) == -2.522786001038096774676288412995370563339e38 - 2.708024460708609732016532185663087200560e38 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: csin (-2 - 3 i) == -9.15449914691142957346729954460983256 + 4.16890695996656435075481305885375484 i":
 ildouble: 1
 ldouble: 1
 Test "Real part of: csin (0.75 + 1.25 i) == 1.28722291002649188575873510790565441 + 1.17210635989270256101081285116138863 i":
 ildouble: 1
 ldouble: 1
+Test "Real part of: csin (0.75 + 11357.25 i) == 8.385498349388321535962327491346664141020e4931 + 9.001213196851067077465606717616495588201e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: csin (0.75 + 710.5 i) == 1.255317763348154410745082950806112487736e308 + 1.347490911916428129246890157395342279438e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: csin (0.75 + 89.5 i) == 2.522786001038096774676288412995370563339e38 + 2.708024460708609732016532185663087200560e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csin (0.75 + 89.5 i) == 2.522786001038096774676288412995370563339e38 + 2.708024460708609732016532185663087200560e38 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: csin (0.75 - 11357.25 i) == 8.385498349388321535962327491346664141020e4931 - 9.001213196851067077465606717616495588201e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: csin (0.75 - 710.5 i) == 1.255317763348154410745082950806112487736e308 - 1.347490911916428129246890157395342279438e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: csin (0.75 - 89.5 i) == 2.522786001038096774676288412995370563339e38 - 2.708024460708609732016532185663087200560e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csin (0.75 - 89.5 i) == 2.522786001038096774676288412995370563339e38 - 2.708024460708609732016532185663087200560e38 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: csin (0x1p-1074 + 1440 i) == 5.981479269486130556466515778180916082415e301 + inf i plus overflow exception":
+double: 1
+idouble: 1
+Test "Real part of: csin (0x1p-16434 + 22730 i) == 1.217853148905605987081057582351152052687e4924 + inf i plus overflow exception":
+ildouble: 1
+ldouble: 1
 
 # csinh
+Test "Imaginary part of: csinh (-11357.25 + 0.75 i) == -9.001213196851067077465606717616495588201e4931 + 8.385498349388321535962327491346664141020e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csinh (-11357.25 - 0.75 i) == -9.001213196851067077465606717616495588201e4931 - 8.385498349388321535962327491346664141020e4931 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: csinh (-2 - 3 i) == 3.59056458998577995201256544779481679 - 0.530921086248519805267040090660676560 i":
 ildouble: 1
 ldouble: 1
 Test "Imaginary part of: csinh (-2 - 3 i) == 3.59056458998577995201256544779481679 - 0.530921086248519805267040090660676560 i":
 double: 1
 idouble: 1
+Test "Imaginary part of: csinh (-710.5 + 0.75 i) == -1.347490911916428129246890157395342279438e308 + 1.255317763348154410745082950806112487736e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csinh (-710.5 - 0.75 i) == -1.347490911916428129246890157395342279438e308 - 1.255317763348154410745082950806112487736e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: csinh (-89.5 + 0.75 i) == -2.708024460708609732016532185663087200560e38 + 2.522786001038096774676288412995370563339e38 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csinh (-89.5 + 0.75 i) == -2.708024460708609732016532185663087200560e38 + 2.522786001038096774676288412995370563339e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: csinh (-89.5 - 0.75 i) == -2.708024460708609732016532185663087200560e38 - 2.522786001038096774676288412995370563339e38 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csinh (-89.5 - 0.75 i) == -2.708024460708609732016532185663087200560e38 - 2.522786001038096774676288412995370563339e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "Real part of: csinh (0.75 + 1.25 i) == 0.259294854551162779153349830618433028 + 1.22863452409509552219214606515777594 i":
 float: 1
 ifloat: 1
 Test "Imaginary part of: csinh (0.75 + 1.25 i) == 0.259294854551162779153349830618433028 + 1.22863452409509552219214606515777594 i":
 float: 1
 ifloat: 1
+Test "Imaginary part of: csinh (11357.25 + 0.75 i) == 9.001213196851067077465606717616495588201e4931 + 8.385498349388321535962327491346664141020e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csinh (11357.25 - 0.75 i) == 9.001213196851067077465606717616495588201e4931 - 8.385498349388321535962327491346664141020e4931 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csinh (1440 + 0x1p-1074 i) == inf + 5.981479269486130556466515778180916082415e301 i plus overflow exception":
+double: 1
+idouble: 1
+Test "Imaginary part of: csinh (22730 + 0x1p-16434 i) == inf + 1.217853148905605987081057582351152052687e4924 i plus overflow exception":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csinh (710.5 + 0.75 i) == 1.347490911916428129246890157395342279438e308 + 1.255317763348154410745082950806112487736e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csinh (710.5 - 0.75 i) == 1.347490911916428129246890157395342279438e308 - 1.255317763348154410745082950806112487736e308 i":
+double: 1
+idouble: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: csinh (89.5 + 0.75 i) == 2.708024460708609732016532185663087200560e38 + 2.522786001038096774676288412995370563339e38 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csinh (89.5 + 0.75 i) == 2.708024460708609732016532185663087200560e38 + 2.522786001038096774676288412995370563339e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
+Test "Real part of: csinh (89.5 - 0.75 i) == 2.708024460708609732016532185663087200560e38 - 2.522786001038096774676288412995370563339e38 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: csinh (89.5 - 0.75 i) == 2.708024460708609732016532185663087200560e38 - 2.522786001038096774676288412995370563339e38 i":
+float: 1
+ifloat: 1
+ildouble: 1
+ldouble: 1
 
 # csqrt
 Test "Real part of: csqrt (-2 + 3 i) == 0.89597747612983812471573375529004348 + 1.6741492280355400404480393008490519 i":
@@ -2266,7 +2546,9 @@ ildouble: 1
 ldouble: 1
 
 Function: Imaginary part of "ccos":
+double: 1
 float: 1
+idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
@@ -2280,7 +2562,9 @@ ildouble: 1
 ldouble: 1
 
 Function: Imaginary part of "ccosh":
+double: 1
 float: 1
+idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
@@ -2392,6 +2676,10 @@ ildouble: 1
 ldouble: 1
 
 Function: Real part of "csin":
+double: 1
+float: 1
+idouble: 1
+ifloat: 1
 ildouble: 1
 ldouble: 1
 
@@ -2410,6 +2698,8 @@ double: 1
 float: 1
 idouble: 1
 ifloat: 1
+ildouble: 1
+ldouble: 1
 
 Function: Real part of "csqrt":
 double: 1